Question
Answer
$$(5+3i)\cdot(9-8i)=-24i^2-13i+45$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5+3i)\cdot(9-8i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}45-40i+27i-24i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-24i^2-13i+45\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5+3i}\right) $ by each term in $ \left( 9-8i\right) $. $$ \left( \color{blue}{5+3i}\right) \cdot \left( 9-8i\right) = 45-40i+27i-24i^2 $$ |
| ② | Combine like terms: $$ 45 \color{blue}{-40i} + \color{blue}{27i} -24i^2 = -24i^2 \color{blue}{-13i} +45 $$ |
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